What I have:
I am using SharePoint online which is part of Office 365.
Question:
What is the best size/ratio of a logo in this case?
(Rectangular one, in type of the old version of SharePoint looks bad and is too small).
Is square the solution? or something like 168 x 80 pixels?
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64x64 .png file is recommended. SharePoint will downsize, but you want to avoid any extra scaling
I've used square, and if it's too big SPO will automatically downsize to fit.
If you really want to change the logo size, you can refer to this article:
http://webbrewers.com/change-logo-size-office-365-sharepoint-2013-public-site/?i=1
